Problem 21 - Algebra 1: Concepts and Skills

Question

NUMBER LINES Use a number line to find the sum. $$ -4+(-7) $$

Step-by-Step Solution

Answer

The sum of -4 + (-7) is -11.

Step 1: Place a dot on -4

Begin by placing a dot on -4 as this is the starting point. This represents the number -4 on the number line.

Step 2: Move 7 units to the left

Since we are adding -7, this is equivalent to subtracting 7, so move 7 units to the left from -4 on the number line. Moving to the left makes the numbers decrease, which corresponds to subtraction.

Step 3: Identify the new position

After moving 7 units to the left of -4, the dot will land on -11. So the sum of -4 + (-7) = -11.

Key Concepts

Addition of Negative Numbers

When you have to add negative numbers, it might seem confusing at first. But it's easier than you think. Just remember that adding a negative number is similar to subtracting a positive number.

For example, if you add

• -4 + (-7), it is like taking 4 away and then another 7 away.

To solve this, place a point at -4 on the number line. Then move left, because we are adding a negative 7. You count 7 spaces, and you end up at -11. So,

• -4 + (-7) = -11.

Adding negative numbers always involves moving to the left if you're using a number line as a visual aid, because it decreases your total. This method provides a clear picture of how addition with negative numbers works.

Integer Operations

Integer operations are the different ways you can combine whole numbers, including both positive and negative numbers. The basic operations include addition, subtraction, multiplication, and division. Today, we focus primarily on addition.

• Adding positive numbers increases the total.
• Adding negative numbers decreases the total.

For example, let's add 5 + (-3). Starting at 5 on the number line:

• You'll move 3 spaces to the left because you're adding a negative number.

You land on 2, so

• 5 + (-3) = 2.

These operations can help when calculating things like temperature changes, financial gains or losses, and even elevations in geography. Always pay attention to the signs of the numbers you're working with, as they dictate the direction of movement on the number line.

Mathematical Visualization

Mathematical visualization helps to see math concepts in action. One of the best tools for understanding integer addition is the number line.

A number line is like a ruler with numbers that go infinitely in both directions. It helps us visualize where numbers start and end, and how they interact when combined.

To use a number line effectively:

• Identify your starting point, like -4 in our example.
• Understand the operation: for -4 + (-7), each unit left represents adding a negative or removing a positive number.
• Draw or visualize the movement. Here, you move 7 spaces left, landing on -11.

Using a number line gives a strong visual connection to abstract mathematical concepts, clarifying how addition of negative numbers works in a visual manner. It’s like turning math into a story that you can see and follow.